U.S. patent number 6,009,629 [Application Number 08/945,797] was granted by the patent office on 2000-01-04 for process for determining the direction of the earth's magnetic field.
This patent grant is currently assigned to Leica Geosystems AG. Invention is credited to Silvio Gnepf, Juerg Weilenmann.
United States Patent |
6,009,629 |
Gnepf , et al. |
January 4, 2000 |
Process for determining the direction of the earth's magnetic
field
Abstract
A method for determining the direction of the Earth's magnetic
field, which may be interfered with by magnetic materials built
into equipment and by electric currents, using an electronic
magnetic compass which contains three magnetic field sensors and
two devices for measuring inclination is provided. The electronic
magnetic compass is arranged in N different spatial positions, in
each of these N positions, the inclination sensor signals and the
magnetic field sensor signals being measured and inclination values
and magnetic field values being determined from these signals. On
the basis of these inclination values and magnetic field values,
the magnitude of the Earth's magnetic field vector is determined
using the vector equation with ##EQU1## N having to be at least
equal to the number of parameters to be determined in the vector
equation.
Inventors: |
Gnepf; Silvio (Heerbrugg,
CH), Weilenmann; Juerg (Widnau, CH) |
Assignee: |
Leica Geosystems AG (Heerbrugg,
CH)
|
Family
ID: |
7788097 |
Appl.
No.: |
08/945,797 |
Filed: |
November 10, 1997 |
PCT
Filed: |
February 10, 1997 |
PCT No.: |
PCT/EP97/00583 |
371
Date: |
November 10, 1997 |
102(e)
Date: |
November 10, 1997 |
PCT
Pub. No.: |
WO97/34125 |
PCT
Pub. Date: |
September 18, 1997 |
Foreign Application Priority Data
|
|
|
|
|
Mar 13, 1996 [DE] |
|
|
196 09 762 |
|
Current U.S.
Class: |
33/357; 33/356;
702/92 |
Current CPC
Class: |
G01V
3/40 (20130101); G01C 17/28 (20130101) |
Current International
Class: |
G01C
17/28 (20060101); G01C 17/00 (20060101); G01V
3/40 (20060101); G01C 017/38 () |
Field of
Search: |
;33/357,304,313,316,319,321,355R,356 ;702/92,150 |
References Cited
[Referenced By]
U.S. Patent Documents
Primary Examiner: Fulton; Christopher W.
Attorney, Agent or Firm: Foley & Lardner
Parent Case Text
CROSS-REFERENCE TO RELATED APPLICATION
This application is the national stage application of
PCT/EP97/00583, filed Feb. 10, 1997, which is entitled to priority
of German Application No. 196 09 762.2-52, filed Mar. 13, 1996.
Claims
We claim:
1. Method for determining the direction of the Earth's magnetic
field, which may be interfered with by magnetic materials built
into equipment and by magnetic fields produced by electric
currents, using an electronic magnetic compass which contains three
magnetic field sensors and two devices for measuring
inclination,
the electronic magnetic compass being arranged in N different
spatial positions,
in each of these N positions, the signals from the devices for
measuring inclination and the signals from the magnetic field
sensors being measured and inclination values and magnetic field
values being determined from these signals, and
on the basis of these inclination values and magnetic field values,
the magnitude of the Earth's magnetic field vector being calculated
using the vector equation
with ##EQU10## N having to be at least equal to the number of
parameters to be determined in the vector equation.
2. Method according to claim 1, characterized in that one of the
following scale definitions
b.sub.g =const.; m.sub.11 =const.; m.sub.11 +m.sub.22 +m.sub.33
=const.;
m.sub.11.sup.2 +m.sub.22.sup.2 +m.sub.33.sup.2 =const.;
m.sub.11.sup.2 +m.sub.12.sup.2 + . . . +m.sub.33.sup.2 =const.; det
m=const.; is selected.
3. Method according to claim 1, characterized in that .DELTA.M=0 is
set if no soft magnetic spurious field is to be taken into
account.
4. Method according to claim 1, characterized in that the magnetic
field vector is determined using an optimization calculation if the
number N of measurements in the various positions is greater than
the number of available equations.
5. Method according to claim 1, characterized in that the magnitude
of the Earth's magnetic field vector is determined using a
statistical optimization method on the basis of the determined
inclination values and magnetic field values with additional use of
the equation
6. Method according to claim 1, characterized in that inclination
sensors are used as the devices for measuring inclination.
7. Method according to claim 1, characterized in that rotational
speed sensors (gyros) are used as the devices for measuring
inclination, the inclination angle being derived by integrating the
rotational speed information.
8. Method according to claim 1, characterized in that encoders,
with which angles are measured with respect to a reference point,
are used as the devices for measuring inclination.
Description
BACKGROUND OF THE INVENTION
1. Field of the Invention
The invention relates to a method for determining the direction of
the Earth's magnetic field, which may be interfered with by
magnetic materials built into equipment and by magnetic fields
produced by electric currents, using an electronic magnetic compass
which contains three magnetic field sensors and two devices for
measuring inclination.
2. Description of the Related Art
U.S. Pat. No. 4,686,772 discloses an electronic magnetic compass
which, for example, is intended to be used to determine the heading
of a tank. The tank has two iron bodies, namely the turret and the
vehicle body, which can rotate relative to one another about a
vertical axis. The magnetic compass is arranged in the vehicle body
and comprises a non-pendulous triaxial magnetometer which outputs
electrical magnetic field signals that represent the three magnetic
field components at the site of the magnetometer. Two inclination
sensors are provided, which output electrical signals that
represent the pitch angle and the roll angle of the vehicle body to
which the inclination sensors are fitted. Further, a device for
measuring angles provides a rotational angle signal for the angle
between the two iron bodies. A plurality of precalibrated
correction factors are stored in a memory, these being intended to
correct the effect of the magnetic field induced by the vehicle on
the measurements by the magnetometer for a plurality of alies of
rotation between the two iron bodies. The heading of the tank is
calculated in real time using a computer on the basis of the
electrical magnetic field signals and the signals from the
inclination sensors, which have been corrected by the stored
correction factors for the corresponding angle of rotation.
Before the described magnetic compass can be used, it is necessary
to carry out calibration measurements. To do this, the vehicle is
arranged on at least two different planes which are not parallel to
one another. In these situations, measurements of the azimuthal
angle, the pitch angle and the roll angle are taken for different
orientations of the vehicle body but the same relative orientation
of the tank turret. In order to make it possible to measure the
last angle, a theodolite, for example, is necessary. During the
calibration, it is assumed that the Earth's magnetic field at the
site of the measurement is known. To do this, the values of the
magnetic inclination and declination of the Earth's magnetic field
for the respective measurement site are taken from cartographic
sources.
U.S. Pat. No. 4,539,760 describes an electronic magnetic compass
for vehicles, which has three magnetic sensors. They respond to the
three orthogonal components of a magnetic field which includes the
Earth's magnetic field and an additional spurious field connected
with the vehicle. The magnetic sensors produce electrical signals
corresponding to the components. Further, inclination sensors
respond to the inclination of the vehicle with respect to the
horizontal plane. A data processing unit and a memory are used to
store signals which are derived as calibration correction values
from the measuring sensors when the vehicle is rotated through a
circle in order to calibrate the magnetic compass. In order to
exclude the effect of the magnetic spurious field, the data
processing unit calculates corrected values for the Earth's
magnetic field at the site of the vehicle, after the calibration
process has been completed and by taking the calibration correction
values into account. The azimuth of the direction of travel of the
vehicle is then calculated on the basis of these corrected values,
using the values from the inclination sensors which are used to
determine the horizon. During the calculations, it is assumed that
the correction matrix is symmetric. This is true only in the rarest
of cases, if ever.
SUMMARY OF THE INVENTION
The object of the invention is to provide a method for determining
the direction of the Earth's magnetic field using an electronic
magnetic compass, which is more straightforward to carry out.
Advantageous refinements of the subject matter of the invention are
also disclosed.
Advantageously, the method according to the invention does not
require any specific calibration measurements using additional
measuring equipment. Neither is it necessary to input special data
in the case of the electronic magnetic compass in order to prepare
it for use. It is merely necessary to arrange the magnetic compass
in arbitrary different positions in space. In each position in
space, three magnetic field components are preferably determined.
These magnetic field components may be mutually orthogonal, if
desired, but do not have to be. Using the inclination values, i.e.
the pitch angle and the roll angle, which are additionally measured
in each position in space, it is possible to determine the
direction of the actual magnetic field vector of the Earth's field
from the respective magnetic field components.
The method according to the invention does not require the
electronic magnetic compass to be calibrated before it is used.
Using the method according to the invention, not only magnetic
spurious fields but also manufacturing tolerances, varying
sensitivities of the sensors, etc. are taken into account. It is
therefore unnecessary to use a magnetic compass already calibrated
by the manufacturer.
In the method according to the invention, use is made of the fact
that the angle of inclination between the gravitation vector and
the Earth's magnetic field vector at the respective fixed site
remains constant independently of the instantaneous position of the
system.
BRIEF DESCRIPTION OF THE DRAWINGS
In order to make the invention easier to understand, figures are
provided in which
FIG. 1 schematically shows an arrangement of an electronic magnetic
compass and soft- and hard-magnetic spurious field sources, and
FIG. 2 represents the vectors relevant for measuring the Earth's
magnetic field.
DESCRIPTION OF SPECIFIC EMBODIMENTS
As early as the 19th century, Poisson addressed the problem of how
to measure the magnetic field which is actually present if a
magnetometer is set up in a system which itself has magnetic
components. Poisson's formula, which describes this situation,
expresses the idea that, in such a case, the magnetic field which
is measured is a linear function of the field that is actually
present, and an affine transformation is thus involved. In
conjunction with this, reference may be made to the abovementioned
U.S. Pat. No. 4,686,772, column 2, lines 26 to 30.
For the general case, it can be stated that the measured magnetic
field is composed of the soft-magnetically distorted Earth's
magnetic field at the measurement site and of a hard-magnetic
component. The soft-magnetically distorted Earth's magnetic field
involves magnetism induced by the Earth's magnetic field. The hard
magnetic component comprises, for example, magnetic fields which
are constant at the site of the magnetometer and are produced by
permanent magnets or electric currents in the system. The hard
magnetic component cannot be affected by a change in the external
field.
In a somewhat different form, the abovementioned Poisson's formula
can be written mathematically as:
with: ##EQU2##
In what is written above, and in the following explanations,
vectors and matrices are written in bold letters. The vectors are
conventionally related to a Cartesian coordinate system. The
matrices are generally 3.times.3 matrices.
FIG. 1 schematically represents the fact that the magnetic compass
DMC is arranged in equipment where permanent magnets, as hard
magnetic interference sources, and soft magnetic materials interact
and affect the value measured by the DMC. FIG. 2 represents the
vectors relevant for measuring the Earth's magnetic field and the
relevant projections into the horizontal plane. In the case of a
magnetic compass arranged fixed in a vehicle, the target direction
corresponds to the heading.
The electronic magnetic compass has three magnetic field sensors
and two inclination sensors, the former determining three magnetic
field components which need not necessarily be mutually
orthogonal.
The permanent magnets and the electric currents produce a field
which is fixed at the site of the magnetic field sensors and has
the effect of an offset of the coordinate system formed by the
magnetic field components.
From a field which is present, the soft magnetic materials produce
an attenuated or amplified field in the field direction and, in
addition, field components in the directions perpendicular thereto.
This can be regarded as "crosstalk" between the field directions x,
y and z.
The same equations as above again arise when considering a
magnetometer which has three non-orthogonal magnetic field sensors
with different sensitivity and an offset, for example an
uncalibrated "raw" magnetometer from the manufacturer.
The measurement of the magnetic field using a "raw" magnetometer of
this type can be expressed mathematically as follows:
with f.sub.i the gain, e.sub.i the measurement direction, i.e. the
unit vector, and o.sub.i the offset of the i-th sensor.
Writing f.sub.i e.sub.i =(M.sub.i1, M.sub.i2, M.sub.i3) and o.sub.i
=b.sub.oi again gives the above equation (1).
In order to determine the value of the Earth's true magnetic field,
it is necessary to solve the abovementioned vector equation (1) for
b.sub.E. Inversion and subtraction give:
with m=M.sup.-1
In order to determine the unknown values M or m=M.sup.-1 and
b.sub.o from equation (1) or (2), a solution method as disclosed by
the abovementioned U.S. Pat. No. 4,686,772 may be adopted. It is
assumed therein that, in each case, the Earth's magnetic field
vector b.sub.E is explicitly known in addition to the measured
magnetic field vector b.sub.mes. The vector equations (1) and (2)
in each case represent a linear equation system for the unknowns
M.sub.ij or m.sub.ij and b.sub.oi. Through measurements in at least
four geometrically different positions, the M.sub.ij and b.sub.oi
are given directly, with a known value of the Earth's magnetic
field, using elementary methods for solving linear equation
systems.
The solution specified in the abovementioned U.S. Pat. No.
4,539,760 is based on the fact that the magnitude of the Earth's
magnetic field is independent of the position of the magnetometer.
If the values m.sub.ij and b.sub.o have been determined correctly,
then a result for the Earth's magnetic field vector b.sub.E is
found which has the same length for each position of the
magnetometer. This gives:
With U.sup.T =U, which means that U is a symmetric matrix.
It can be directly seen that, using this equation (3), it is only
possible to calculate the product U=m.sup.T m of the desired matrix
m. Only if it is assumed that this matrix is symmetric, and with
the supposition that the diagonal is positive, can the elements of
this matrix be calculated. However, the former assumption is true
only in the rarest of cases, since it would imply a soft magnetic
symmetry, which is extremely improbable in technical equipment, for
example an aircraft or motor vehicle.
According to the invention, the approach then adopted for
determining the value b.sub.E, i.e. to solve the vector equation,
is one in which use is made of the fact that, for each position of
the measuring system at a given geographical site, the angle
between the horizontal plane and the Earth's magnetic field, i.e.
the inclination angle, remains constant. This is then clearly also
true for the angle between the direction of the gravitation vector
g and the Earth's magnetic field vector b.sub.E. The following can
thus be written:
with ##EQU3## in which i is the inclination angle.
This equation means that the component of the magnetic field vector
in the direction of the Earth's gravitational field, that is to say
perpendicular to the horizontal plane, remains the same for all
positions of the system.
The value m occurs linearly in this equation, and not as a product.
The gravitation vector g can be determined using the inclination
sensors.
For this reason, this value m can be calculated directly, without
needing to take a measurement of the field, as in the
abovementioned U.S. Pat. No. 4,686,772, or having to assume special
symmetry conditions, as in the abovementioned U.S. Pat. No.
4,539,760.
The number of parameters to be determined is:
m=3.times.3=9
b.sub.o =3
b.sub.g =1.
This gives a total of 9+3+1=13 parameters, determination of which
requires at least 13 equations.
An arbitrary scale factor can further be selected as disclosed, for
example, by the abovementioned U.S. Pat. No. 4,539,760 (column 4,
line 3 et seq.). Possible ways of defining the scale include, for
example, those in the following list:
b.sub.g =const.
m.sub.11 =const.
m.sub.11 +m.sub.22 +m.sub.33 =const.
m.sub.11.sup.2 +m.sub.22.sup.2 +m.sub.33.sup.2 =const.
m.sub.11.sup.2 +m.sub.12.sup.2 + . . . +m.sub.33.sup.2 =const.
det m=const.
or other suitable ones, it also being possible for the constant to
be selected as 1. The definition of the scale reduces the number of
parameters by 1, so that only 12 parameters then remain, for which
a corresponding number of equations is needed. During the initial
calibration of the magnetic compass, 12 different geometrical
positions j=1, . . . , 12 are adopted therefor, in which the three
magnetic field components and the two inclination angles are
measured.
A linear equation system:
is obtained, with u.sub.o =m b.sub.o and, for example, b.sub.g =1
which then explicitly gives:
If more than 12 equations are available then, for example, the best
fit can be determined in this case using the generally known least
squares method.
Within the scope of the invention, it is also possible to use the
fact that the inclination angle or b.sub.g is constant for a given
fixed site, together with the fact that the magnetic field vector
has a constant length L(b.sub.E)=.vertline.b.sub.E .tbd.In other
words, this means that not only equation (5) which was given above
but also equation (3) can be used for the method. In this case, the
parameter L(b.sub.E) must also be determined, so that the number N
of parameters and therefore the number of measurements needed is
increased by 1 to N=13.
Advantageously, using equations (3) and (5) provides better
utilization of the available data, since each measurement is used
in two equations. The number of measurements needed is therefore
halved. In order to carry out this method, it is necessary to use a
statistical fitting calculation which, for example, may be based on
the least squares method.
In the method described below, the abovementioned equations (3) and
(5) are used in statistically correct fashion.
The relationship which exists between the magnetic field sensor
signals .mu..sub.ij : i=1, 2, 3 and the Earth's magnetic field
vector b.sub.Ej, will be explained in more detail below. It can be
represented by the equation
(Measuring Positions) ##EQU4## measured values from the 3 magnetic
field sensors in position j ##EQU5## vector for offset and hard
magnetic spurious field ##EQU6## soft magnetic distortion matrix
##EQU7##
The components of the Earth's magnetic field vector b.sub.Ej are
unknown in the various positions of the magnetic compass. It is,
however, possible to describe them partially using the inclination
sensors. In this case, each of the two inclination sensors measures
one component of the gravitational field vector normalized to 1.
The direction of this vector is vertical. ##EQU8## g.sub.1j,
g.sub.2j : measured values from the inclination sensors, g.sub.3j
=(1-g.sub.1j.sup.2 -g.sub.2j.sup.2).sup.1/2
The values of the parameters M.sub.11 . . . M.sub.33, .mu..sub.01,
.mu..sub.02, .mu..sub.03, .alpha..sub.1 . . . .alpha..sub.N and i
can be determined using an optimization calculation known per se,
for example by finding the minimum for the statistical sum ##EQU9##
Various other solution methods are possible in the scope of the
invention, for example using Kalman filters, fuzzy logic or neural
networks.
It can thus be seen that there is a substantial mathematical
simplification if the value .DELTA.M=0. This is the case when no
soft magnetic spurious field needs to be taken into account. M then
corresponds to the unit matrix.
In the above description, reference was made to inclination
sensors. Instead of these, it is also possible to use two
orthogonally mounted encoders. These would be used to measure
angles with respect to a reference point. In practical embodiment,
however, it would then be necessary to provide a frame which is
mounted fixed, and with respect to which the magnetic compass and
the interfering system would rotate.
It would also be possible to determine the desired inclination
angles using two rotational speed sensors, i.e. gyros, fitted to
the system. The angles of rotation can be derived by integrating
the rotational speed information.
* * * * *